As soon as the tributes begin to the filmed, the Games truly begin. The arena is only the final stage of the Games (although, Katniss soon discovers that the Games are never over for the winners). Being on camera allows the tributes to gain support and sympathy, making them more appealing to sponsors. Also, since the Capital wants a big show, the more dynamic they are on camera, the more likely they are to get attention and sponsors. We discover that the key to surviving isn't necessarily being the best in the arena, but the most liked, and therefore the most sponsored. Since the Games are all about the show, being filmed also means that if you aren't doing something entertaining, the Game Makers are likely to send something entertaining to you.
Being filmed makes the entire Games an act, or illusion. The tributes are only pawns, however, and the information they have is limited. It seems like this would make it harder to accept their fate. First, they are under the illusion that their is a "winner," which Katniss discovers to be false. Also, they are often mislead about their popularity, and therefore odds of winning. The tributes from the wealthier districts tend to believe themselves to have higher odds, but as the Games progress, this also proves to be false. Finally, since everything is set up as a "show," especially in the pregame ceremonies, the reality of death, murder, etc. hits the Tributes hard once they are in the arena. Up until this point, they have been viewing the Games as just that - games. Suddenly, it all becomes real, and not all the Tributes are able to adjust accordingly.